Parts of Exponential Equations

Equations of Exponential Functions

Equations of Exponential Functions

•  $f\left(x\right)=a\left(b\right)^x$  

• a: represents the y-intercept  (0,a)

• b: represents the base

• Exponential Growth: if base is greater than 1, the graph will be increasing

• Exponential Decay: if base is less than 1, the graph will be decreasing

Example

 $f\left(x\right)=4\left(5\right)^x$  

• y-intercept: (0,4)

• base: 5 

• exponential growth because the base 5 is greater than 1

Example

 $g\left(x\right)=2\left(\frac{1}{3}\right)^x$  

• y-intercept: (0,2)

• base: 1/3 

• exponential decay because the base 1/3 is less than 1

Multiple Choice

Is the pictured graph growth, decay, or linear or none?

• Exponential Growth

• Exponential Decay

• Linear

• None

Multiple Choice

Is the function an example of exponential growth or decay?

$$f\left(x\right)=\frac{1}{2}\left(6\right)^x$$  

• Exponential Growth

• Exponential Decay

Multiple Choice

Is the function an example of exponential growth or decay?

$$f\left(x\right)=7\left(\frac{2}{3}\right)^x$$  

• Exponential Growth

• Exponential Decay

Multiple Choice

Is this an example of exponential growth or decay?

• Exponential Growth

• Exponential Decay

Multiple Choice

Is the function an example of exponential growth or decay?

$$f\left(x\right)=2\left(\frac{5}{4}\right)^x$$  

• Exponential Growth

• Exponential Decay

Multiple Choice

Pick the equation that is exponential decay

• $$f\left(x\right)=200\left(0.88\right)^x$$

• $$g\left(x\right)=5\left(1.88\right)^x$$
  

Multiple Choice

Pick the equation that is exponential growth

• f(x )=2(0.5)^x

• g(x) = 0.5(2)^x

Multiple Choice

What type of function is

$$f\left(x\right)=2\left(\frac{1}{7}\right)^x$$  

• Exponential Growth

• Linear

• Exponential Decay

• None of the Above

Multiple Choice

Is this exponential growth or decay?

• Growth

• Decay

Multiple Choice

What is the y-intercept represented by the equation e(x) = 10(5)^x

• (0,5)

• (5,0)

• (10,0)

• (0,10)

Multiple Choice

What is the y-intercept represented by the equation

$$f\left(x\right)=3\left(7\right)^x$$  

• (0,3)

• (3,0)

• (7,0)

• (0,7)

Multiple Choice

What is the y-intercept represented by the equation

$$f\left(x\right)=\frac{1}{3}\left(2\right)^x$$  

• (0,2)

• (0,1/3)

• (1/3,0)

• (2,0)

Multiple Choice

What is the y-intercept represented by the equation

$$g\left(x\right)=\left(4\right)^x$$  

• (0,4)

• (4,0)

• (0,0)

• (0,1)

• (1,0)

Multiple Choice

Is the pictured graph growth, decay, or linear or none?

• Exponential Growth

• Exponential Decay

• Linear

• None

Multiple Choice

Which the following graphs shows an exponential decay equation?